Only b/c it's not made for brewing, I would not recommend it.
I used to just wash the bottles with no additives on a "sanitizing" cycle of heated wash, and heated dry that my washer offers. Then I started using a bottle rinsing gadget with StarSan just prior to loading the dishwasher, and I dump the leftover StarSan into the washer. Preston recently suggested spraying the inside with StarSan which I just added to the pre-game routine. (We clean/rinse our dishes well before washing, so the washer itself stays fairly clean.)